WO1995002291A1 - Dispositif de precodage ameliore et methode de precodage associee - Google Patents

Dispositif de precodage ameliore et methode de precodage associee Download PDF

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Publication number
WO1995002291A1
WO1995002291A1 PCT/US1994/007109 US9407109W WO9502291A1 WO 1995002291 A1 WO1995002291 A1 WO 1995002291A1 US 9407109 W US9407109 W US 9407109W WO 9502291 A1 WO9502291 A1 WO 9502291A1
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Prior art keywords
sequence
trellis code
channel output
components
operably coupled
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PCT/US1994/007109
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English (en)
Inventor
M. Vedat Eyuboglu
Original Assignee
Codex Corporation, A Subsidiary Company Of Motorola Inc.
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Application filed by Codex Corporation, A Subsidiary Company Of Motorola Inc. filed Critical Codex Corporation, A Subsidiary Company Of Motorola Inc.
Priority to CA002142846A priority Critical patent/CA2142846C/fr
Priority to DE69433224T priority patent/DE69433224T2/de
Priority to EP94921369A priority patent/EP0672321B1/fr
Priority to JP50404295A priority patent/JP3547443B2/ja
Publication of WO1995002291A1 publication Critical patent/WO1995002291A1/fr

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Classifications

    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/38—Synchronous or start-stop systems, e.g. for Baudot code
    • H04L25/40—Transmitting circuits; Receiving circuits
    • H04L25/49—Transmitting circuits; Receiving circuits using code conversion at the transmitter; using predistortion; using insertion of idle bits for obtaining a desired frequency spectrum; using three or more amplitude levels ; Baseband coding techniques specific to data transmission systems
    • H04L25/497—Transmitting circuits; Receiving circuits using code conversion at the transmitter; using predistortion; using insertion of idle bits for obtaining a desired frequency spectrum; using three or more amplitude levels ; Baseband coding techniques specific to data transmission systems by correlative coding, e.g. partial response coding or echo modulation coding transmitters and receivers for partial response systems
    • H04L25/4975—Correlative coding using Tomlinson precoding, Harashima precoding, Trellis precoding or GPRS
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/02—Details ; arrangements for supplying electrical power along data transmission lines
    • H04L25/03—Shaping networks in transmitter or receiver, e.g. adaptive shaping networks
    • H04L25/03006—Arrangements for removing intersymbol interference
    • H04L25/03343—Arrangements at the transmitter end
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L25/00—Baseband systems
    • H04L25/38—Synchronous or start-stop systems, e.g. for Baudot code
    • H04L25/40—Transmitting circuits; Receiving circuits
    • H04L25/49—Transmitting circuits; Receiving circuits using code conversion at the transmitter; using predistortion; using insertion of idle bits for obtaining a desired frequency spectrum; using three or more amplitude levels ; Baseband coding techniques specific to data transmission systems
    • H04L25/497—Transmitting circuits; Receiving circuits using code conversion at the transmitter; using predistortion; using insertion of idle bits for obtaining a desired frequency spectrum; using three or more amplitude levels ; Baseband coding techniques specific to data transmission systems by correlative coding, e.g. partial response coding or echo modulation coding transmitters and receivers for partial response systems
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L27/00—Modulated-carrier systems
    • H04L27/32—Carrier systems characterised by combinations of two or more of the types covered by groups H04L27/02, H04L27/10, H04L27/18 or H04L27/26
    • H04L27/34—Amplitude- and phase-modulated carrier systems, e.g. quadrature-amplitude modulated carrier systems
    • H04L27/3405—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power
    • H04L27/3411—Modifications of the signal space to increase the efficiency of transmission, e.g. reduction of the bit error rate, bandwidth, or average power reducing the peak to average power ratio or the mean power of the constellation; Arrangements for increasing the shape gain of a signal set

Definitions

  • This invention relates generally to digital communication systems, and more particularly to precoding a digital data sequence for transmission in a digital communication system.
  • DFE zero-forcing decision-feedback equalization
  • ISI intersymbol interference
  • trellis precoding is effective only for signal constellations whose signal points are uniformly distributed within a space-filling boundary region.
  • Space-filling substantially means that a union of proper non-overlapping translations of the boundary region may cover (tile) the entire space.
  • the boundary region must be representable as a fundamental region of a lattice, typically referred to as a precoding lattice.
  • a precoding lattice is typically chosen as a scaled version MZ 2 of a two-dimensional integer lattice Z 2 (where M is a scaling factor) such that the boundary region then has the shape of a square.
  • square signal constellations are not desirable, since they have a higher two-dimensional peak-to-average power ratio (PAR) than constellations with more circular boundaries. More importantly, square constellations are not suitable for representing fractional bits per symbol and require a method known as constellation switching to allow fractional rate transmission, which further increases the two-dimensional PAR.
  • PAR peak-to-average power ratio
  • trellis precoding it is possible to find precoding lattices whose Voronoi region is more circular than that of a square and which accommodates certain fractional data rates. However, this approach is not very flexible, since it does not uniformly handle all fractional data rates and is more difficult to make invariant to 90° phase rotations, which is an important requirement in certain practical applications.
  • Another drawback of trellis precoding is that to achieve shaping gain, the precoding operation must be combined with shaping operations, which increases the complexity of implementation.
  • a device and method are set forth for mapping a digital data sequence into a signal point sequence x(D) for transmission over a channel characterized by a nonideal channel response h(D) using a trellis code C comprising,
  • a mapper for mapping the digital data sequence into a signal point sequence u(D) such that a component u k of u(D) at a given time k is selected based in part on past components ⁇ Y k - ⁇ .
  • Y k - 2 »— ⁇ °f a channel output sequence y(D) x(D)h(D) based on feedback information provided by a precoder, and
  • ISI intersymbol interference
  • FIG. 1 is a block diagram of a device in accordance with the present invention.
  • FIG. 2 is a more detailed block diagram illustrating a first embodiment of a device in accordance with the present invention.
  • FIG. 3 is a detailed block diagram of the mapper of FIG. 2.
  • FIG. 4 is a block diagram of a second embodiment of a device in accordance with the present invention.
  • FIG. 5 is a block diagram of a first embodiment of a digital communication system utilizing a device in accordance with the present invention.
  • FIG. 6 is a block diagram of a recovery unit of the digital communication system of FIG. 5, showing the recovery unit with more particularity.
  • FIG. 7 is a flow diagram setting forth steps of one embodiment in accordance with the method of the present invention.
  • FIG. 8 is a flow diagram setting forth steps of another embodiment in accordance with the method of the present invention.
  • FIG. 9 is a block diagram of a digital signal processor used for precoding a digital data sequence to obtain a sequence x(D) for transmission over a discrete-time channel with an impulse response h(D) in accordance with the present invention.
  • the method and device of the present invention permits precoding a digital data sequence for transmission over a digital communication channel, performing particularly well on channels having severe attenuation distortion.
  • Substantial benefits are obtained by utilizing the present invention: transmission at substantially any desired data rate without constellation switching, transmission with circular signal constellations, simplification of shaping by completely separating shaping from precoding, and reduction of dither loss by selecting the output of the mapper based in part upon the past components of a channel output sequence based on feedback information provided by a precoder.
  • the code C is a 2n-dimensional trellis code, where n is an integer, based on a lattice partition ⁇ / ⁇ ', where ⁇ is a preselected lattice and ⁇ ' is a preselected sublattice of ⁇ , and a rate m/m+r convolutional code.
  • the device (100) includes a mapper (102) and a precoder (104).
  • a characteristic of the precoding scheme is that the precoded sequence x(D) may be represented by the sum
  • u(D) u 0 + u ⁇ O + u 2 D 2 +.... is a signal point sequence representing the digital data and is provided by the mapper
  • ISI intersymbol interference
  • a feature of the present invention is that the components
  • the coset is therefore selected based on the state s k of the code sequence y(D).
  • the digital data determines the signal points from the selected coset as usual.
  • Information about the past values ⁇ y k _ ⁇ , y k _ 2 ⁇ is provided to the mapper (102) by the precoder (104), which is operably coupled to the mapper (102).
  • the technique of the present invention differs from a technique described in "ISI coder - Combined coding and precoding," AT&T contribution to EIA-TR 30.1 , Baltimore, MD, June 1993, in important ways.
  • the components u are always chosen from a translate of the time-zero lattice ⁇ 0 regardless of the state s k of y(D), while the components c k are selected from one of 2 r cosets of ⁇ 0 depending on the state s k .
  • the technique of the present invention is logically simpler since the selection of c k utilizes the same lattice all the time.
  • the method of the present invention may be made transparent to 90 degree rotations (see below), whereas this cannot be achieved completely in the above-referenced technique.
  • the present invention is utilized where the complex impulse response h(D) has no zeroes on the unit circle, or equivalent ⁇ , when its inverse, 1/h(D), is stable. Therefore, the following embodiments utilize an h(D) that is a canonical response with a stable inverse.
  • the response h(D) has been determined and is known at the transmitter and the receiver.
  • FIG. 2, numeral 200 is a more detailed block diagram of a first embodiment of a device in accordance with the present invention.
  • the digital data sequence is first mapped in a mapper (102) into a signal point sequence u(D) using any combination of known encoding, mapping and shaping techniques.
  • the precoder comprises a first combining unit (204) and a filtering/modulo unit (206).
  • the filtering/modulo unit (206) includes a filter (212) operably coupled to receive x(D) and is utilized for generating d(D).
  • the components c k are chosen from ⁇ ⁇ such that the average energy of the dither sequence d(D) is kept small.
  • the channel output sequence y(D) will be a valid code sequence, provided that u k 's are chosen from an allowable coset of the time-zero lattice based on the current state s k of y(D) in the trellis code.
  • the sublattice ⁇ s is chosen to obtain a good trade-off between complexity and performance.
  • ⁇ s may be selected to be an n-fold Cartesian product of a two-dimensional lattice.
  • the trellis code is a four-dimensional trellis code that is based on the lattice partition RZ 4 /2D 4 .
  • the mapper will also include a differential encoder which is well-known in the state-of-the-art (e.g., L F. Wei, "Trellis-coded modulation using multi-dimensional constellations," IEEE Trans. Inform. Theory, vol. IT-33, pp. 483- 501 , July 1987).
  • a differential encoder which is well-known in the state-of-the-art (e.g., L F. Wei, "Trellis-coded modulation using multi-dimensional constellations," IEEE Trans. Inform. Theory, vol. IT-33, pp. 483- 501 , July 1987).
  • the average energy S x of the transmitted sequence x(D) will be approximately the same as the energy S u of the signal sequence u(D) as long as the average dither energy Sd is small. That means, the better the approximation c(D) » p(D) is, the smaller will be the increase in average energy due to the dither sequence d(D). This is achieved by choosing the elements of d k from a fundamental Voronoi region of the sublattice ⁇ s .
  • a key advantage of the present invention is that the dither energy is reduced by modifying the sequence u(D) based on the past history of the channel output sequence y(D).
  • FIG. 3 shows a more detailed block diagram of the mapper (102) which shows a code tracker (304) which is utilized to determine the cosets of ⁇ 0 from which the components u k are selected.
  • the input to the code tracker (304) is the channel output sequence y(D) obtained from the precoder (104).
  • the code tracker (304) includes a coset information extractor (302) for receiving y(D), a bit mapper
  • a rate m/r ⁇ +1 convolutional encoder is used to produce one extra bit once every two symbols, and this bit is used to select one of two cosets of the time-zero lattice RD 4 in RZ 4 , while the data bits select a four-dimensional point from that coset.
  • FIG. 4 shows an alternative embodiment, numeral 400, of the present invention which is substantially equivalent to the first embodiment shown in FIG. 2.
  • Information about the sequence y(D) provided by the precoder is used by the code tracker (310) in the mapper (102) to determine the coset of the time-zero lattice ⁇ 0 from which the mapper output u is selected.
  • the sublattice RD4 may be represented as a union of the 4D lattice 2Z 4 with its coset 2Z 4 + (0, 0, 1 ,1 ).
  • the 4D lattice 2Z 4 can be obtained by taking a Cartesian product of the two-dimensional (2D) lattice 2Z 2 which consists of all pairs of even integers. Therefore RD4 is represented as
  • the invention is not limited to criteria that minimize the average dither energy, and any criterion may be used to select the code sequence c(D) as long as the selection of each c ⁇ is based only upon past values XJ, j ⁇ i, of x(D), and the components c k belong to the time-zero lattice ⁇ 0 .
  • it may be desirable to limit the range of the channel output symbols yi ui + Cj. This may be achieved, at the expense of a higher dither energy S , by restricting the values of q to a certain range.
  • a canonical receiver front-end that includes a whitened matched filter and a sampler (in the case of continuous-time channels) operating at a selected symbol rate may be utilized to provide such an equivalent channel.
  • h(D) represents the combined effect of the filters in the transmitter, channel, the receiver, and a sampler.
  • w(D) represents the noise after it passes through the receive filters and the sampler.
  • the whitened-matched filter reduces the strength of the distortion through proper filtering and therein lies the performance advantage of the present invention over conventional linear equalizations.
  • a whitened matched filter may be determined adaptively using standard adaption techniques for decision-feedback equalizers.
  • h(D) be an all-pole filter
  • a first embodiment of a device of the present invention incorporated into a digital communication system is illustrated in the block diagrams of FIG. 5, numeral 500, wherein at least one of a transmission unit and a receiving unit utilizes the present invention.
  • the said system typically includes at least one of a transmission unit (502) and a receiving unit (506) wherein the transmission unit has a mapper (508) and a precoder (510) for transmitting a digital data sequence and a channel (504) obtained as described in the above paragraph, operably coupled to the precoder (510), for facilitating transmission of the precoded sequence x(D), and the receiving unit (506) has a decoding unit (518), operably coupled to the channel unit (504), for receiving and decoding a received sequence r(D) to provide an estimated output sequence y(D), and a recovery unit (520), operably coupled to the decoding unit (518), for substantially recovering an estimate u(D) of the signal point sequence u(D). An estimate of the transmitted digital data sequence is then found from
  • the decoding unit (518) is typically a decoder for the trellis code C, as is known in the art.
  • the decoding unit (518) typically receives and decodes a noisy received sequence r(D) which is of a form:
  • a recovery unit (520), operably coupled to the decoding unit (518), substantially recovers an estimate u(D) of the input sequence u(D), described more fully below.
  • sequence y(D) must be a sequence in the trellis code C. That means that the sequence y(D) may be estimated by a conventional decoder for C, as is known in the art, to provide an estimated output sequence y(D).
  • the digital communications receiver may be selected such that the decoding unit (518) further includes a reduced complexity sequence estimator unit that utilizes a correlation between successive symbols yi.
  • the reduced complexity sequence estimator unit utilizes a sequence estimator having a reduced number of states that are determined utilizing state merging techniques for reduced-state sequence estimation (RSSE).
  • the recovery unit may be selected to include a range violation determiner unit.
  • a range violation determiner unit When an i'th variable UJ of the recovered sequence u(D) is outside a certain range (a range violation), this unit adjusts at least one of an estimate yi and a past estimate yk-j (where j is a positive integer) to substantially correct the range violation.
  • FIG. 7, numeral 700 sets forth a flow chart illustrating steps in accordance with the method of the present invention for precoding a stream of signal points for transmission in a digital communication system.
  • the method provides for precoding a digital data sequence to generate a sequence x(D) for transmission over a discrete-time channel with an impulse response h(D) using a trellis code C.
  • ISI post-cursor intersymbol interference
  • y(D) is a code sequence in the trellis code.
  • the components c k of c(D) are selected from a sublattice ⁇ s of the time-zero lattice ⁇ 0 of the trellis code. The sequences are as described above.
  • the components c k of c(D) are selected from a sublattice ⁇ s of the time-zero lattice ⁇ 0 of the trellis code.
  • the present invention may be implemented in a digital communication system, illustrated in FIG.
  • a digital signal processor (902) is utilized to precode a digital data sequence to obtain a sequence x(D) for transmission over a discrete-time channel with an impulse response h(D).
  • the code sequence c(D) is determined based upon only the post-cursor ISI sequence p(D).
  • the components c k of c(D) are selected from a sublattice ⁇ s of the time-zero lattice ⁇ 0 of the trellis code. Further description of the operation of the processor follows that described above.
  • the sequence u(D) is chosen based in part on past components
  • the present invention may be utilized with virtually any signaling method and at any data rate. Further, the present invention may be utilized independently of constellation shaping techniques (e.g., shell mapping, "Signal mapping and shaping for V.fast,” Motorola contribution D196, CCITT Study Group XVIII, Geneva, June 1992); that means u(D) may represent an already shaped sequence whose signal points have a nonuniform Gaussian-like probability distribution.
  • constellation shaping techniques e.g., shell mapping, "Signal mapping and shaping for V.fast," Motorola contribution D196, CCITT Study Group XVIII, Geneva, June 1992.
  • the dither sequence may increase the average transmit energy. Since in practice, the average transmit energy must be kept constant, the signal x(D) must be scaled down to maintain the same average energy. The increase in the average transmit energy is referred to herein as a dithering loss.
  • the method may be used with block or lattice codes as well. It may also be used with selected multi-level trellis codes. Also, although two-dimensional (passband, quadrature) transmission systems are emphasized, the methods may also be applied to one-dimensional (baseband) or higher-dimensional (parallel channels) transmission systems. Further, the invention may be utilized with trellis codes whose dimensionality is odd.
  • channel responses h(D) that are monic
  • the invention may also be applied to more general channel responses with ho ⁇ 1 , by either scaling the channel response to make it monic, or by appropriately scaling the variables of ' the precoding system. All such implementations are considered substantially equivalent to the present invention.

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  • Engineering & Computer Science (AREA)
  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
  • Physics & Mathematics (AREA)
  • Spectroscopy & Molecular Physics (AREA)
  • Power Engineering (AREA)
  • Error Detection And Correction (AREA)
  • Dc Digital Transmission (AREA)

Abstract

Technique de précodage améliorée (700) et appareil associé (100). Il s'agit de transmettre une séquence de points d'un signal sur un canal h(D) de façon à assurer un transfert efficace de l'information en présence de brouillage entre symboles et de bruit, et à un débit approchant de la capacité du canal. Ladite technique fonctionne en modulation codée en treillis, et avec toute constellation (502) de signaux. Cette invention simplifie donc la mise en forme et autorise des transmissions de signaux à des débits fractionnaires sans commutation de constellations. L'un de ses avantages clefs par rapport à la technique antérieure réside dans sa capacité de réduction des pertes par tremblement en sélectionnant les composantes de sortie d'un mappeur en se basant sur les composantes antérieures d'une séquence de sortie d'un canal.
PCT/US1994/007109 1993-07-08 1994-06-24 Dispositif de precodage ameliore et methode de precodage associee WO1995002291A1 (fr)

Priority Applications (4)

Application Number Priority Date Filing Date Title
CA002142846A CA2142846C (fr) 1993-07-08 1994-06-24 Dispositif et methode de precodage ameliores
DE69433224T DE69433224T2 (de) 1993-07-08 1994-06-24 Verbesserte einrichtung und verfahren zur prekodierung
EP94921369A EP0672321B1 (fr) 1993-07-08 1994-06-24 Dispositif de precodage ameliore et methode de precodage associee
JP50404295A JP3547443B2 (ja) 1993-07-08 1994-06-24 改良されたプリコーディング装置および方法

Applications Claiming Priority (2)

Application Number Priority Date Filing Date Title
US08/089,319 1993-07-08
US08/089,319 US5446758A (en) 1993-07-08 1993-07-08 Device and method for precoding

Publications (1)

Publication Number Publication Date
WO1995002291A1 true WO1995002291A1 (fr) 1995-01-19

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US (1) US5446758A (fr)
EP (1) EP0672321B1 (fr)
JP (1) JP3547443B2 (fr)
CA (1) CA2142846C (fr)
DE (1) DE69433224T2 (fr)
WO (1) WO1995002291A1 (fr)

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EP0675622A2 (fr) * 1994-04-01 1995-10-04 Fujitsu Limited Procédé et système pour la transmission d'un signal vectoriel codé avec réduction de la puissance du signal
FR2746993A1 (fr) * 1996-03-31 1997-10-03 Fujitsu Ltd Procede d'appreciation et appareil de precodage

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US5604769A (en) * 1994-10-13 1997-02-18 Lucent Technologies Inc. Hybrid equalizer arrangement for use in data communications equipment
US5602583A (en) * 1995-02-10 1997-02-11 Zenith Electronics Corporation NTSC rejection filter with switched tomlinson precoder for reducing NTSC co-channel interference in ATV receivers
US5878077A (en) * 1995-10-10 1999-03-02 Paradyne Corporation Apparatus for high-speed simultaneous voice/data communications
US6031873A (en) * 1996-06-24 2000-02-29 3Com Corporation Nested shell mapping
JP3634082B2 (ja) * 1996-08-29 2005-03-30 富士通株式会社 送信装置および受信装置
US6081555A (en) * 1996-12-04 2000-06-27 Conexant Systems, Inc. Methods and apparatus for implementing shell mapping techniques in the context of a PCM-based modem communications system
US6307893B1 (en) * 1997-03-05 2001-10-23 Paradyne Corporation System and method for transmit signal spectral shaping
US6101223A (en) * 1997-03-06 2000-08-08 Paradyne Corporation System and method for optimizing the uncoded modulation of circular constellations using circular precoding and nonlinear encoding
US6252911B1 (en) * 1997-06-11 2001-06-26 Texas Instruments Incorporated Trellis shaping for PCM modems
US5995543A (en) * 1997-06-30 1999-11-30 Stmicroelectronics N.V. Constrained fixed delay tree search receiver for a MTR=2 encoded communication channel
US6061407A (en) * 1997-10-08 2000-05-09 International Business Machines Corp. Transmission method and apparatus employing trellis-augmented precoding
US6201836B1 (en) * 1999-01-20 2001-03-13 Motorola Inc. Method and apparatus for combining a Trellis coding scheme with a pre-coding scheme for data signals
US6529558B1 (en) * 1999-05-27 2003-03-04 Zenith Electronics Corporation Coding and decoding a signal modified in accordance with the feedback states of an encoder
US7000175B2 (en) * 2000-11-03 2006-02-14 Agere Systems Inc. Method and apparatus for pipelined joint equalization and decoding for gigabit communications
CN1463500A (zh) * 2001-05-22 2003-12-24 皇家菲利浦电子有限公司 解码变长码字序列的方法
US8165189B2 (en) * 2005-10-07 2012-04-24 University Of Washington Through Its Center For Commercialization Dirty paper precoding with known interference structure at receiver
US7831892B2 (en) * 2007-01-20 2010-11-09 Harris Corporation Generic, reduced state, maximum likelihood decoder
US7831893B2 (en) * 2007-01-20 2010-11-09 Harris Corporation Reduced state trellis decoder using programmable trellis parameters

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US5329551A (en) * 1992-04-16 1994-07-12 At&T Bell Laboratories Overlapped multilevel codes

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Cited By (6)

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Publication number Priority date Publication date Assignee Title
EP0675622A2 (fr) * 1994-04-01 1995-10-04 Fujitsu Limited Procédé et système pour la transmission d'un signal vectoriel codé avec réduction de la puissance du signal
EP0675622A3 (fr) * 1994-04-01 1999-11-17 Fujitsu Limited Procédé et système pour la transmission d'un signal vectoriel codé avec réduction de la puissance du signal
US6104758A (en) * 1994-04-01 2000-08-15 Fujitsu Limited Process and system for transferring vector signal with precoding for signal power reduction
FR2746993A1 (fr) * 1996-03-31 1997-10-03 Fujitsu Ltd Procede d'appreciation et appareil de precodage
US6078624A (en) * 1996-03-31 2000-06-20 Fujitsu Limited Judging method and a precoding apparatus
GB2311913B (en) * 1996-03-31 2000-11-22 Fujitsu Ltd A judging method and a precoding apparatus

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DE69433224T2 (de) 2004-04-29
US5446758A (en) 1995-08-29
DE69433224D1 (de) 2003-11-13
CA2142846A1 (fr) 1995-01-19
JPH08501433A (ja) 1996-02-13
EP0672321A4 (fr) 2000-03-15
JP3547443B2 (ja) 2004-07-28
EP0672321A1 (fr) 1995-09-20
EP0672321B1 (fr) 2003-10-08
CA2142846C (fr) 1999-09-07

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